Diffuse reflection boundary condition for high-order lattice Boltzmann models with streaming–collision mechanism

Meng, Juan; Zhang, Yonghao

doi:10.1016/j.jcp.2013.10.057

Cited by 45 publications

(23 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because the diffuse boundary condition can capture velocity slip while the bounce-back scheme produces non-slip boundary condition, it is not surprising that the LBM with diffuse boundary condition perform better in the slip regime [46,47]. The DVM data show that the analytic solution derived from the Stokes approximation with the Maxwell's slip boundary condition [48] is valid when K n l 0.05.…”

Section: Lbm_d2q9 Dvm_d2q16 Dvm_d2q36 Dvm_d2q64 Dvm_d2q1600mentioning

confidence: 98%

Pore-scale simulations of rarefied gas flows in ultra-tight porous media

Zhu

et al. 2019

Fuel

Self Cite

View full text Add to dashboard Cite

An in-depth understanding of gas transport in ultra-tight porous media is the key to quantifying flow properties of shale rocks with pore space as small as a few nanometers, where the gas rarefaction effects play a major role. As the conventional fluid mechanics theory fails to describe non-equilibrium rarefied flow, we resort to the gas kinetic theory and directly simulate gas flow inside the porous media utilising the digital images of porous media where the pore space is resolved. The Boltzmann model equation is solved by the discrete velocity method (DVM), which can accurately predict the permeability enhancement caused by rarefaction effects. Our simulations for different porous media show that the commonly-used standard lattice Boltzmann method (LBM) cannot describe rarefaction effects, although the kinetic boundary condition, which helps to capture velocity-slip, can extend the validity of the LBM to the slip flow regime. The heuristic Klinkenberg-type models proposed for all the flow regimes often involve many unknown empirical parameters, which may be calibrated by our simulations. However, these parameters are different for each porous medium and also depend on flow conditions, so these models are not of any prac-1 tical use. By contrast, our kinetic solver can accurately predict apparent permeability without introducing any empirical parameters, which lays firm foundation for upscaling. As the large flow paths with least flow resistance dominate the overall permeability, the requirement on the velocityspace resolution is significantly reduced for our DVM simulations to predict accurate permeability with affordable computational costs, which offers a promising new way for digital rock analysis.

show abstract

Section: Lbm_d2q9 Dvm_d2q16 Dvm_d2q36 Dvm_d2q64 Dvm_d2q1600mentioning

confidence: 98%

Pore-scale simulations of rarefied gas flows in ultra-tight porous media

Zhu

et al. 2019

Fuel

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, high-order contributions f (n) α (n ≥ 1) of the CE expansion do not contribute to the macroscopic density and flow velocity. By inserting the CE ansatz (28) and (29) into the Boltzmann equation (27) we find the general solution for n ≥ 1…”

Section: A Chapman-enskog Analysismentioning

confidence: 99%

High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers

Feuchter

2016

Phys. Rev. E

View full text Add to dashboard Cite

We analyze a large number of high-order discrete velocity models for solving the Boltzmann-BGK equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.

show abstract

“…(23) is combined with high-order velocity sets in which case ghost sites may be required for complex boundary conditions. See, for instance, Meng and Zhang [35]. 053310-5…”

Section: A High-order Discretization Of the Streaming Termmentioning

confidence: 99%

Consistent lattice Boltzmann equations for phase transitions

Mattila

2014

Phys. Rev. E

View full text Add to dashboard Cite

Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

show abstract

Diffuse reflection boundary condition for high-order lattice Boltzmann models with streaming–collision mechanism

Cited by 45 publications

References 34 publications

Pore-scale simulations of rarefied gas flows in ultra-tight porous media

Pore-scale simulations of rarefied gas flows in ultra-tight porous media

High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers

Consistent lattice Boltzmann equations for phase transitions

Contact Info

Product

Resources

About